Question

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Age   Bone Density
34   357
45   341
48   331
60   329
65   325

Age   Bone Density
34   357
45   341
48   331
60   329
65 325

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 4 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ

Step 5 of 6: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

The statistical software output for this problem is:

From above output:

1) Slope = -0.964

2) Intercept = 385.180

4) Change in dependent variable = b1 = -0.964

5) True

6) Coefficient of determination = 0.859